The Writing an Essay How to Have Subtitles Game

<h1>The Writing an Essay How to Have Subtitles Game </h1> <p>With the correct sort of training, you can definitely upgrade your business English article composing abilities. Not editing shows your educator that you're uninterested in quality work, and this could prompt a terrible evaluation. At the point when it is for some post-graduate class, it is anything but difficult to twofold that. It is to ensure the contemplating unknown dialect system is viable. </p> <h2>Life, Death, and Writing an Essay How to Have Subtitles </h2> <p>Essays are significantly shorter than books. Most importantly, the titleeven a concise onecan give perusers a lot of setting about a paper. </p> <p>Writing a paper is a serious simple and precarious occupation, at precisely the same second. Exposition design doesn't have anything to do with the genuine substance of the article, it is the manner in which you sort out and present it. Right paper design is a piece of cake in the event that you read the remainder of this report. </p> <h2>Lies You've Been Told About Writing an Essay How to Have Subtitles </h2> <p>There are different private venture report composing tips which can likewise assist you with figuring out how to make a remarkable report. You're ready to discover more data from modest paper composing administration is a reliable and client agreeable composing administration. There are bunches of reference and catalog styles and you can promptly get to their principles on the web. Perfect exposition composing administration site. </p> <p>You'll know the manner in which your composing is seen by others and what activities to make the most appropriate sort of effect on the most reasonable people. On the off chance that you wish to see how to make an association document, you must get the hang of everything about the key segments to be incorporated. Obviously, when you're investigating an issue which influences another country, you should be seeing that country's significant news site. In the absolute initial segment, the creator centers around a particular issue, why it's significant and should be examined. </p> <p>Another idea which ought to be talked about is a caption that could likewise thought of as a subheading. To begin with, it's required to introduce an exhaustive clarification of the two thoughts referenced already. Beside that, it's profoundly urged to utilize an assortment of subheadings just on the condition your examination paperhas two and more subsections inside a greater area. The charming thing that should be referenced is that they weren't allowed to utilize the key headings and subheadings in their conventional works. </p> <h2>The Chronicles of Writing an Essay How to Have Subtitles </h2> <p>The best strategy to examine if it's the book is appropriate to what you're expounding on is to check through the file. Solid information, the believability of subtleties, and uncommon configuration will consistently establish an enduring connection. In the first place, it's essential to find which sort of reports is required for a particular goal. Attempt to recall that the objective of utilizing headings is to keep up your peruser on target. </p> <h2>Writing an Essay How to Have Subtitles at a Glance </h2> <p>A organized technique is welcome here. Particularly with respect to making a program. Keep in mind the centrality of editing your work since the objective is to comprehend what you're examining to achieve your intended interest group. The ability to encode rules and to distinguish rule-disregarding occasions from the focal point of consideration is basic for versatile conduct. </p> <h2> Writing an Essay How to Have Subtitles Fundamentals Explained </h2> <p>Your second passage should then express the technique by which the paper will be composed. The key issue to be referenced is that every single one of both paper positions has certain rules which ought to be followed. From that point onward, return to the paper and rehash it to ensure the paper sounds legitimate and you're content by it. In the event that a discussion paper was discharged, proceed to find the paper and read it. </p> <h2> The Demise of Writing an Essay How to Have Subtitles</h2> <p>Report composing is significant for the development of each business as the evaluation of specific issues, monetary tasks and conditions should be cultivated in a particular report composing arrangement to work. Discovering how to make an extraordinary private company report, an individual should tak e note of that it's an all around organized truthful paper that covers an examination of the issue or circumstance with the extra suggestions. It is basic to express the foremost issues, investigate, and legitimize particular contentions on the inquiry. To get a viable report, consistently hold fast to the best possible system. </p> <p>No new material should be incorporated and models shouldn't be given. It's additionally regularly less hard to gain a point clear by utilizing shorter sentences, which are slanted to be less difficult to peruse. Another negative point is that there are a few movies and arrangement scenes promptly accessible, that you may end up resting short of what you need. Endeavor to find intriguing guides to delineate your most significant focuses. </p> <p>Ensure you execute the right utilization of transitional words. It can flexibly the extra data with respect to the words being verbally expressed by methods for a character. In the event that you don't comprehend a word which have been expressed by the on-screen character, you can think about the caption, it enables hearing debilitated people to comprehend a film. Long sentences are to some degree increasingly entangled to develop appropriately. </p>

Investment and Portfolio Management Risk-Sensitive Investment

Question: Talk about the Investment and Portfolio Management forRisk-Sensitive Investment. Answer: Presentation Venture is characterized as the utilization, which includes buying resources, giving a credit or keeping of assets in ledger to protect what's to come. The principle focal point of doing a venture is to produce future returns in which one can depend on particularly during the old. In addition, it is likewise an arrangement to setting up better lives for the family. A nation does interest so as to shield eventual fate of its residents. Ideas of Investment One of the significant ideas utilized in comprehension of venture is economy. This is on the grounds that each venture is involved in the arrangement of new and gainful capital. This capital is required to be in a structure, which is helpful and produces ventures, which are solid and long haul in its usefulness. A case of such is plant and apparatus. Furthermore, budgetary speculation is likewise among fundamental ideas in adventure. It is a sort of venture, which is assigned in financial terms and asset (Chellaraj Mattoo, 2015, p. 8). It is relied upon to yield returns over a give n timeframe. It is encouraged through trade of cases, for example, shares, debentures, investment funds, premiums, and fixed stores (Davis Lleo, 2015, p. 21). Speculation Approach Speculation approaches are characterized into four units. The first is the momentary high need venture goals. It is a venture which factors in high need in accomplishing of specific goals in a brief timeframe. This can be working of a house for living. The subsequent one is the drawn out high need speculation. This alludes to venture booked to be acknowledged at future date however it is worked for from a delicate date. A case of this is the retirement advantages and training of the kids. Thirdly is the low-need. These have low venture instrument. The last methodology is the moneymaking targets. This is a sort of speculation involved in putting away of surplus cash and boosting of riches. It very well may be done through visiting and buying of pointless extravagances vehicle. History of Singapore Exchange Singapore is a nation situated in mainland Asia. Its trade showcase is called Singapore Exchange Limited (SEL). It was framed on December 1, 1999 as a holding organization. After its arrangement, portions of the organizations, for example, Stock Exchange of Singapore were dropped and the offers were given completely were given to this new organization. Different organizations who used to exchange the trade market of Singapore (Singapur, 2014, p. 23) at first possessed the offers being moved. This trade organization falls under the Asian and Oceania trade league. As indicated by the ongoing insights gave by KOH, it is concluded that it overwhelms the stock trade in the two mainlands (Koh, 2014, p. 25). It offers various types of assistance, which are identified with security trade, exchanging, and subsidiaries among numerous others. In the year 2000, it was recorded as the subsequent trade house in the Asian-Pacific locale getting both open and private benefit of trade. Later in 2010, it went into merger contracts with Australian Security Exchange (ASE). This was spread by quick development in PC innovation in Australia. The significant investors in this restricted obligation organization of Singapore are SEL property. This organization holds 23.66% of the complete portions of the organization. DBS Nominees is a privately owned business in Singapore and part of investors of Singapore Exchange Limited. Its offers are aggregately 9.85% (Chellaraj Mattoo, 2015, p. 42). Besides, DBSN administrations Pte restricted is likewise an incredible financial specialist in this trade firm. It holds 5.70% of offers in the organization. Citibank Nominees likewise have a state in the running and the board of this security organization with shares moderately 18.55% of the complete offers. In conclusion, it is the HBSN Company having near 7.16% offers in the Singapore Exchange (Koh, 2014, p. 23). Activity of Singapore Exchange As indicated by examine, Singapore Exchange Limited apparently owns and work protections and subsidiaries and their related items in the nation. Aside from its tasks in the nation, it has interfaces in different nations, for example, China, Thailand, and Australia. It gives the beneficial protections of handling and data innovation administrations to the members in the money related markets in an unequivocal and solid way (Wong, 2014, p. 27). Items This organization is situated in exchanging of protections, subsidiaries, and items. Moreover, it likewise manages clearing and settlement of swaps for their customers. It has the obligation of performing obligations managing vault and intermediary administrations to its individuals at a moderate valuing system. Subsidiaries are one of the primary organizations being dove on in this organization (Koh, Chang Koh, 2014, p. 16).They are turned out dependent on the more extensive scope of Asian resources, which begin from Chinese condition to the Indian cash in the locale. This permits high respecting the ravenous financial specialists through presenting them to a difficult to-purchase showcase idea in the trade model. This has empowered Asian speculators to get venture openings (Ong et al, 2015, p. 41). This helped them in amplifying associations with their partners who are presented to less improvements however more quickly developing markets in the mainland Asia and Oceania. Through t his instrument of exchanging determines, Singapore has built up a connection with HongKong and Shangai so as to take into consideration simple buying from one another with sole point of boosting benefits. They likewise need to cut on the cost, which emerges in the occasion where one is specified to exchange from organizations in which they don't accomplice in any capacity. Through the examination, Thailand has shut worked with bank of china with sole point of advancing items from Thailand. As indicated by J.P Morgan, this has expanded rivalry and the business in the stock trade ascended to 9%, which is collection of 28.8 million agreements (Thomsett, 2015, p. 24). Protections are additionally part of the incredible worry in any traded advertise. As per the measurements created rearward in the SEL, protections slapped at half, which is comparative with 1.8 billion offers per day. This depended on the quarterly framework from the earlier year, which was 2015.This prompted a battle with the point of pulling in expensive postings that were involved to drive exchanging exercises the nation. The brokers in the security showcase were evaluated to possess in any event 7.7% of the protections yearly which when changed over to Singapore dollars it is moderately 7.82. In this way, it prompted presentation of arrangement of major developments which incorporate circuit breakers, liquidity suppliers and the market markers (Davis Lleo, 2015, p. 28). Wares Singapore Commodity Exchange (SICOM) is appraised to giving of profoundly and the most proficient commercial center for exchanging of prospects and clearing organizations in Singapore. It is reasoned to selling of enormous and items whose source is of demonstrated quality to adjust advertise costs in the exchanging zone. So as to look after this, they needed to create activities, which are client neighborly. This instrument is through contribution of the best conditions in the nation for a functioning discount exchanging. This have a marked down cost and along these lines numerous customers are tempted to purchase from them. Thus, the market is enlarged inconclusive (Lim, 2011, p. 15). The exchanging volume of over of about 27.6 million was acknowledged because of this technique for commitment in the market. These invigorate them to start speculations on grain and land creates as they are uncommon and they are exceptionally gainful. The grain business is generally modest with least d angers inclusion. Portfolio Management Portfolio is characterized as the spreading of dangers where the financial specialist will undoubtedly understanding during the business residency. This is done through the gathering of money related speculations, for example, securities, money counterparts, and stocks and different things associated with exchanging stock trade advertise. Portfolio is held legitimately by the speculator or the monetary projector of the business. As a rule, it is developed by the hazard resistance of the business one is putting resources into. Most speculators who bomb in business do so as a result of absence of information in the securities exchange. The administrators should build up a system of overseeing portfolio in the organizations they run so as to evade the devastation brought by unanticipated cataclysms in the business world (Ong et al, 2015, p. 53). The Asians nations ought to consistently be frightened because of proceeds with increase in the United States of America dollar. They are quali fied for manage their organizations through execution of Federal Reserves so as to help in controling dangers during downturn period. This is conceivable since it much unsurprising because of the way that United States is most grown monetarily than some other nation on the planet. Additionally, it is judicious for Asians nations to contribute prior before the loan fee heightens because of thankfulness in dollar by getting of advances from budgetary establishments on schedule. This is a result of the predicted likelihood in debilitating of their cash and in this manner the monetary guidelines may devalue. Moreover, Asian speculators should grasp on the remote trade holds since this incredibly helps in countering of the difficulties realized by the debilitate of their monetary forms. This will assist them with being strong in the occasions when the capital inflows are knowledgeable about the nation. To add on this, the nation ought to take part in organizing of the changes which have a superior effect on its speculators. This will make a space for loads of speculation openings and in this manner make the nation a venture goal (Wong, 2011, p. 22). By making such a situation, a ton of dangers will be kept away from. This will move the diagram of the speculation ra tes towards the positive measurement financially. R

Loreal Company Background

Organization Background Fresh out of a French concoction designing school, youthful business visionary Eugene Schueller built up a hair color with tints beauticians all through Paris couldn’t stand up to. The one-item adventure he propelled in 1909 has since developed into the world’s biggest beautifying agents organization: L’Oreal. L’Oreal started its worldwide extension during the second 50% of the twentieth Century, and now offers hair care, hair shading, healthy skin, cosmetics, and scents in 130 nations. Its 23 brands incorporate drug store staples L’Oreal, Garnier, and Maybelline, just as upscale brands Yves Saint Laurent, Redken, and the Kiehl’s healthy skin line. L’Oreal as of late extended its produce suite by getting the dermatological magnificence care brand Skinceuticals in 2005, and retail location The Body Shop the next year. Today, the organization utilizes in excess of 65,000 individuals in eight offices: activities, fund, data frameworks and innovation, advertising, business and deals, correspondence, HR, just as innovative work. In excess of 2,900 pros work in L’Oreal’s R&D office, which studies skin and hair and utilizations its discoveries to create more secure and increasingly powerful items to improve excellence and ensure skin. The R&D authorities working in the company’s 18 research habitats have foundations in 30 fields, including science, science, medication, material science, physical science, and toxicology. L'Oreal grows in excess of 3,000 new equations for every year. L’Oreal’s duty to decent variety, honesty, obligation and regard for individuals and the earth earned it a spot on Ethisphere Magazine’s rankings of the world’s most moral organizations in 2007. Its items mirror a pledge to serving the necessities of different populaces, including men and African Americans. In 2001, the organization propelled Mizani, a hair care brand grew explicitly for remarkable ethnic hair types. For corporate social duty, the organization has sanctioned a few network and ecological projects, from giving work chances to incapacitated understudies in Taiwan to diminishing water and vitality use at processing plants far and wide to making a HIV/AIDS backing and instruction program for representatives in South Africa.

Digital Transformation And Its Effect On A Business Essay

Digital transformation reshapes each side of a business. As digital technology continues to evolve, i feel that booming digital transformation would force careful collaboration, thoughtful coming up with, and therefore the inclusion of each department. During recent years, we’ve seen shifts in however ancient leadership roles operate, as silos break down and therefore the scopes of varied roles widen and alter. Digital transformation has morphed from a trend to a central element of recent business strategy. Here square measure the highest ten trends I expect to ascertain in 2017: 1. ability is a lot of very important to success than ever: amendment goes to happen whether or not you pursue it or not—you solely ought to consider however the role of cloud computing in 2016 has evolved to know. trendy enterprises succeed once they adapt to trade and marketplace shifts and incorporate new technology into company culture and regular operations. However, digital transformation isn’t solely concerning technology, it’s concerning transferral along the ability of technology with a culture that embraces the amendment that it will lead for the organization. 2. Growing importance of the user expertise: The client experience (including employees) is that the final goal of any digital transformation. Customers square measure a lot of cautious than ever; they’ll retreat from brands that don’t align with their values and desires. A top-notch user expertise may be a fantastic thanks toShow MoreRelatedDigital Transformation Research Paper729 Words   |  3 PagesChanging Role of HR in Digital Transformation IoT and advanced technologies are expected to replace all the conventional tools and systems at the workplaces with their digitized versions by 2022 in all the top ten economies of the world. Now, the question arises, do the traditional businesses are ready to adopt digital transformation? 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Decision Tree Free Essays

string(62) " an outside opinion on a decision the company must make soon\." Decision Trees A Primer for Decision-making Professionals By Rafael Olivas 2007 Decision Trees A Primer for Decision-making Professionals ii Decision Trees A Primer for Decision-making Professionals Table of Contents Section Page Preface†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦ iv 1. 0 Introduction†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. We will write a custom essay sample on Decision Tree or any similar topic only for you Order Now 1 1. 1 Advantages of using decision trees †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. 1 1. About this primer†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. 1 1. 3 To use this primer†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. 2 Decision Scenario †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. 3 2. 1 Describe decision alter natives and outcomes†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦ 4 2. 1. 1 The first decision (root node)†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. 4 2. 1. Chance outcomes †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. 5 2. 1. 3 Endpoints and payoffs †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦ †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦ 5 2. 0 2. 2 Incorporate uncertainty (outcome probability) †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦ 7 2. 3 Find the expected value (EV)†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. 8 2. 4 Add a sequential decision †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. 0 2. 4. 1 Construct a decision tree †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦ 10 2. 4. 2 Recalculate the expected values †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦ 11 2. 4. 3 Analyze the changes †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. 13 3. 0 Basic Concepts†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. 4 3. 1 Decision tree notation (nodes and branches) †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. 14 3. 1. 1 3. 1. 2 3. 1. 3 3. 1. 4 Decision nodes and the root node†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. 15 Chance nodes †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦ 15 Endpoints†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. 5 Branches †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. 15 3. 2 3. 3 3. 4 3. 5 4. 0 5. 0 Payoff values†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. 16 Outcome probability†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. 17 Expected value †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦ 18 Decision tree analysis †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. 0 Glossary †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦ 23 More to Explore †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. 26 iii Decision Trees A Primer for Decision-making Professionals Preface Decision trees find use in a wide range of disparate applications. They are used in many different disciplines including medical diagnosis, cognitive science, artificial intelligence, game theory, engineering, and data mining. Despite this trend surprisingly few good, clear introductions to basic decision tree concepts are available. The present work attempts to meet that need by offering a concise primer for novices. Acknowledgments The author gratefully acknowledges instructor Meryl Natches, CEO of TechProse, for invaluable editing, guidance, and patience. The author also thanks the Technical Communication 1 class participants at UC Berkeley Extension during the spring semester 2007 for review and comments. Rosana Francescato tested the material for clarity and provided helpful feedback in the development of this project. CJ Kalin, Ph. D. , introduced me to the decision tree method in a Project Risk Management class at UC Berkeley Extension. Her real-world examples demonstrated how the decision trees technique helps solve complex project management problems. Despite the aforementioned contributions the author accepts responsibility for any errors or omissions herein. Please send feedback to rafael@projectsphinx. com All trademarks are the property of their respective holders. Microsoft ® , Excel ®, and Word ® are registered trademarks of Microsoft Corporation Rev. 5, 04/05/07  © 2007, Rafael Olivas v Decision Trees A Primer for Decision-making Professionals v Decision Trees A Primer for Decision-making Professionals 1. 0 Introduction A decision tree is a method you can use to help make good choices, especially decisions that involve high costs and risks. Decision trees use a graphic approach to compare competing alternatives and assign values to those alternatives by combining uncertainties, c osts, and payoffs into specific numerical values. If you are a project manager, business analyst, or a project decision-maker, this primer is for you. If you are interested in cognitive science, artificial intelligence, data mining, medical diagnosis, formal problem solving, or game theory, this primer provides an introduction to basic concepts of decision tree analysis. 1. 1 Advantages of using decision trees Decision trees offer advantages over other methods of analyzing alternatives. They are: †¢ Graphic. You can represent decision alternatives, possible outcomes, and chance events schematically. The visual approach is particularly helpful in comprehending sequential decisions and outcome dependencies. †¢ Efficient. You can quickly express complex alternatives clearly. You can easily modify a decision tree as new information becomes available. Set up a decision tree to compare how changing input values affect various decision alternatives. Standard decision tree notation is easy to adopt. Revealing. You can compare competing alternatives—even without complete information—in terms of risk and probable value. The Expected Value (EV) term combines relative investment costs, anticipated payoffs, and uncertainties into a single numerical value. The EV reveals the overall merits of competing alternatives. Complementary. You can use decision trees in conjunction with other project management tools. For example, the decision tree method can help evaluate project schedules. †¢ †¢ 1. 2 About this primer This primer offers an introduction to basic decision tree analysis. After studying this material for an hour, most users will be able to understand and apply decision tree analysis to solve simple and even moderately complex decision problems. You can readily construct and analyze simple decision trees such as those found in this primer with pen, paper, and a calculator. However, a spreadsheet such as Microsoft Excel can dramatically facilitate setting up and modifying decision trees. A number of other software applications are also available. These range from low-cost Microsoft Excel plug-ins to more expensive dedicated applications. For the purposes of this primer, a pen, paper, and calculator are sufficient. 1 Decision Trees A Primer for Decision-making Professionals 1. 3 To use this primer You can use this primer in several ways. If you prefer to get started immediately with drawing and using decision tree notation, then begin with the Decision Scenario, an exercise that puts you in the role of using a decision tree in step-by-step fashion. If you are more comfortable learning by first seeing how a process works, then start with Basic Concepts. Whichever way you begin, make sure to review both of these sections. The Glossary defines underlined terms. After you review the concepts and use the scenario exercise, you can find external references in More to Explore. Icons indicate items of special interest: †¢ †¢ †¢ †¢ Example Exercise Note Tip 2 Decision Trees A Primer for Decision-making Professionals 2. 0 Decision Scenario Consider the following scenario. Really Big Ideas, Inc. a small company that develops inventions for the consumer market, has recruited you as a consultant to make a recommendation on a critical business decision. At 10:00 a. m. , you meet Adam Smith, the Vice President in charge of product development. Smith expresses his wish for an outside opinion on a decision the company must make soon. You read "Decision Tree" in category "Essay examples" Your job is to supply such an informed opinion. Smith tells you that a short meeting will provide all the information needed and introduce the project managers for two possible (and competing) products. As Smith ushers you into a conference room he also mentions that he expects your analysis by 11:00 a. m. , scarcely an hour from now! You are given pen, paper, and a calculator. At 10:05 a. m. , you and Smith enter a small meeting room. Smith explains that Really Big Ideas has a three-month window of opportunity to develop a new product using new pattern recognition software the company recently created. Surprisingly, the software adapts easily to different applications. Really Big Ideas only has the resources and time to develop one of two projects, or to develop none. Project Managers Aisha Ali and Ben Bertrand arrive. After brief introductions, Aisha Ali launches her pitch. She says that a smoke and fire detector is the best project to make. The detector goes beyond ordinary smoke detectors. It can detect flames as well as smoke. It will cost $100,000 to develop, and if it succeeds the Business Analysis department says it will generate revenue of $1,000,000. Not to be outdone, Ben Bertrand announces that a motion detector device is the best project to develop. The motion detector, which uses conventional household lighting, will only cost $10,000 to develop. He adds that the analysts expect such a device to generate $300,000 in revenue. Smith asks if you have any questions, so you carefully ask about the chances for success. Both project managers agree that Samiksha Singh, the Director of the Business Analysis department, has that information. Smith initiates a conference call with Samiksha Singh. Singh informs the meeting that the smoke and fire detector has a 50% chance of success, and that the motion detector has an 80% chance of success. Smith thanks all the participants and ends the meeting. It is now 10:30 a. . Smith announces that he’ll return within the hour to see if you have decision analysis. Smith leaves you with your notes, paper, pen, and a calculator. Can you help Really Big Ideas to decide which product, if either, to develop? How can you evaluate the alternatives in a measurable way given the various uncertainties involved? You can use a decision tree to describe and then to evaluate the decision alternatives. 3 D ecision Trees A Primer for Decision-making Professionals 2. 1 Describe decision alternatives and outcomes You can now start your decision tree. A decision tree is a diagram of nodes and connecting branches. Nodes indicate decision points, chance events, or branch terminals. Branches correspond to each decision alternative or event outcome emerging from a node. 2. 1. 1 The first decision (root node) Start by drawing a small square on the left side on a piece of paper. This is called the root node, or root. The root node represents the first set of decision alternatives. For each decision alternative draw a line, or branch, extending to the right from the root node. Allow a generous amount of space between the lines to add information. Some branches may split into additional decision alternatives or outcomes. You can also â€Å"bend† branches so that the lines line up horizontally. These techniques make keeping track of alternatives easier. (See figure 2. 1. 1) Label each branch with the decision and its associated investment cost. Write that the smoke and fire detector will cost (-$100,000) to develop. Similarly, write that the motion detector will cost (-$10,000) to develop. Write $0 at the third branch corresponding to the alternative to develop neither product. Tip Show the costs as negative values since they represent a â€Å"preliminary loss. Any future gross revenue will be offset by costs. Showing costs as negative values simplifies the calculation of payoff. Figure 2. 1. 1 The root node is the small square at the left. Branch lines emerge from the root towards the right. Each branch represents one decision alternative. 4 Decision Trees A Primer for Decision-making Professionals 2. 1. 2 Chance outco mes In the Really Big Ideas scenario each product development effort can have one of two outcomes: each project can either succeed or fail. Draw a small circle, or chance node, at the end of the branch for the smoke and fire detector. Draw a chance node at the end of the branch for the motion detector. From each chance node draw two branches towards the right; one branch represents success and the other represents failure. Label the branches accordingly. Figure 2. 1. 2 Chance nodes, shown as small circles, lead to two or more possible outcomes. Draw each outcome as a branch from the chance node. 2. 1. 3 Endpoints and payoffs You can now complete all the branches with endpoints, since there is no further branch information to represent. Draw a small triangle ( ) at the end of each branch to represent the endpoint. Write the payoff value at the endpoint. In business applications the payoff is usually a monetary value equal to the anticipated net profit, or return on investment. Net profit (or net loss) is the difference between the investment cost and the total revenue. A positive value indicates a net profit, while a negative value indicates a net loss. In other words, if revenue exceeds investment, then the effort is profitable. Otherwise the effort is a net loss, or a breakeven result if the payoff is zero. For Really Big Ideas, a successful smoke and fire detector project will earn $1,000,000 in gross revenue. The resulting net profit therefore equals the sum of the gross revenue and the investment cost. Recall that cost can be represented as a negative number. The calculation is therefore $1,000,000 + (-$100,000) = $900,000 net profit, or payoff. Write $900,000 at the end of the branch for success of the smoke and fire detector. 5 Decision Trees A Primer for Decision-making Professionals However, if the smoke and fire detector project is not successful, then no revenue will be earned and all the investment will be lost. The calculation for this event is $0 + (-$100,000) = (-$100,000), a loss or negative payoff. Write (-$100,000) at the end of the branch for failure of the smoke and fire detector. Perform a similar calculation for the success and failure payoffs for the motion detector. Your results should show a $290,000 payoff if successful, and a (-$10,000) payoff (a loss) if it fails. Write these values at the endpoints of their respective branches. The payoff for the decision branch to not develop either project is simply $0. See figure 2. 1. 3. Figure 2. 1. 3 Use endpoints, shown by small triangles with one point connecting to the branch, to indicate that there are no further outcomes or decisions to consider. Write payoff values for each terminated branch to the right of the endpoints. This concludes the basic structure of the decision tree for the Really Big Ideas alternatives. We can now incorporate the likelihood of success and failure and use that to analyze the decision alternatives. 6 Decision Trees A Primer for Decision-making Professionals 2. 2 Incorporate uncertainty (outcome probability) You can now incorporate the relative outcome probability, or uncertainty, associated with each chance event. You can express probabilities as percentages or as decimal fractions. This primer adopts the common decision tree convention of using decimal fractions from (0. 0) to (1. 0), in which (1. 0) = 100%. In the Really Big Ideas scenario, the smoke and fire detector has a 50% chance of success, and therefore a 50% chance of failure. Therefore, write (0. 5) on the success branch and (0. 5) on the failure branch. The motion detector has an 80%, or (0. 8) chance of success, and therefore a 20%, or (0. 2) chance of failure. Write these values on their respective branch lines. See figure 2. 2. Figure 2. 2 Write the probability for each outcome branch. You can express a probability as a decimal fraction in parentheses. Decision Trees A Primer for Decision-making Professionals 2. 3 Find the expected value (EV) You are now ready to evaluate the relative merits of each decision alternative. Expected value (EV) is the way to combine payoffs and probabilities for each node. The higher the EV, the better a particular decision alternative on average when compared to the other alternatives in the decision tree. You calculate the EV for any chance node by summing together all the EVs for each branch that is connected to the node. The general formula for calculating EV at any chance nodes is given as: EVchance node = EVbranch1 + EVbranch2 + . . + EVbranchN †¢ †¢ †¢ In the Really Big Ideas scenario, if the smoke and fire detector is successful, the EV is the payoff (profit) multiplied by its probability, or $900,000 x 0. 5 = $450,000. The EV if the fire detector project fails is (-$100,000) x 0. 5 = (-$50,000). The EV for the decision to develop the smoke and fire detector (incorporating both success and failure) is the sum of the EV for all the eventualities. EVnode = (EVsuccess + EVfailure) = $450,000 + (-$50,000) = $400,000. Similarly, the EV for the decision to develop the motion detector is given by EV = ($390,000 x 0. 8) + [(-$10,000) x 0. ] = $310,000. Figure 2. 3. Expected value (EV) is the sum of all the combined payoffs and pro babilities for each chance node. †¢ Write the EV for each node near that node. See figure 2. 3. 8 Decision Trees A Primer for Decision-making Professionals The smoke and fire detector project has a higher EV than the motion detector. You can report the analysis with these summarized presentation points: †¢ The smoke and fire detector is the better project to develop, despite the greater risk. The significantly larger anticipated profits make the risk more acceptable than the competing project. The motion detector is less risky, but also significantly less profitable. With the given profit expectations the project does not overcome the expected value of its rival project. Exercise Try different possible payoff and/or probability combinations to raise the EV for the motion detector. What combinations would make this EV superior to the smoke and fire detector? Note Do not confuse EV with any particular payoff amount that would be earned for any specific instance of the gambit . EV is only the average payoff if the trial were repeated many times. Many real-world decisions do not have the advantage of being repeatable. Nevertheless, probabilities can still be assigned to outcomes based on information from expert judgment and other means of risk analysis. Such methods are beyond the scope of this primer. For the purposes of this primer assume that the examples use realistic probabilities from reliable sources. 9 Decision Trees A Primer for Decision-making Professionals 2. 4 Add a sequential decision Consider the following information, which continues the Really Big Ideas decision scenario. Vice President Adam Smith of Really Big Ideas, Inc. calls you the following day. He reports that the company has learned new information that may affect the decision. Smith wants to know if you can prepare a new analysis using the new information. Smith tells you that the proposed smoke and fire detector must pass an Underwriters Laboratories (UL) safety certification before it can be sold. (Such certification is not necessary for the motion detector). Director Samiksha Singh has interviewed a UL inspector and learned how the certification process works. Singh has modified the marketing and success estimates based on the new information. She now reports the following: †¢ A commercial grade certification will result in $1,000,000 sales (as originally expected). However, the likelihood of obtaining the coveted commercial certification is only 30% due to the stringent standard. †¢ †¢ A less-stringent residential grade certification is 60% likely, but would result in only $800,000 sales. There is a 10% chance that the smoke and fire detector will not pass any certification test. In this case—a complete failure—the company will lose the initial $100,000 investment cost. Underwriters Laboratories charges a $5,000 non-refundable fee for the certification application. †¢ Your job is to construct and then evaluate a new decision tree based on this new information. . 4. 1 Construct a decision tree Begin the revised decision tree at the left and through the first chance event nodes as in the prior version. The results for the motion detector and no project remain unchanged. The chance node for the successful development of the smoke and fire detector can now lead to a new decision node; represent this new decision node wi th a small square. The decision at this node is whether to submit an application for the UL safety certification. There are only two choices possible: submit an application, at an investment of $5,000, or do not submit an application. You may guess that failure to submit the application after successful project development does not make good sense, and this is correct. The decision tree shows that your guess is correct. You â€Å"resolve† decision nodes in terms of the branch with the highest EV. Therefore a â€Å"failure to submit application† branch does not play a role in the value of its decision node. The â€Å"submit application† path leads to one of three possible outcomes: commercial grade, residential grade, or no certification. The probability of each outcome is 0. 3, 0. 6, and 0. 1 respectively. Write these probabilities on their respective branches. 0 Decision Trees A Primer for Decision-making Professionals The commercial grade outcome terminates with a payoff calculated as follows: revenue + development cost + application cost = $1,000,000 + (-$100,000) + (-$5,000) = $895,000. In a similar way, the residential grade outcome terminates with this payoff: $800,000 + (-$100,000) + (- $5,000) = $695,000. If the device does not earn a certification it cannot be sold with a UL certification. This situation dooms its marketing prospects to no revenue and a loss of the investments. In that case: $0 + (-$100,000) + (-$5,000) = (-$105,000), a loss. Write each payoff near the matching endpont as you calculate its value. See figure 2. 4. 1. Figure 2. 4. 1 This is an example of a sequential decision. The original root decision leads to at least one other decision on some branch path. The second decision leads to further chance events. Add decision nodes representing how they must occur in time on a branch path. A decision tree can help you keep track of many such sequential decisions. 2. 4. 2 Recalculate the expected values You are now ready to find the EV for the chance event node representing the UL safety certification. Recall that for any chance node, EVchance node = [EVbranch1 + EVbranch2 + . . . +EVbranchN]. 11 Decision Trees A Primer for Decision-making Professionals Therefore, ($895,000 x 0. 3) + ($695,000 x 0. 6) + [(-$105,000) x 0. 1] = $675,000. This chance node is thus resolved or collapsed into a single EV, in this case $675,000. Now use this amount as the payoff value for the â€Å"submit application† branch of its decision node. You may notice that the â€Å"don’t submit application† branch also can have an expected value, in this case (-$100,000). You resolve a decision node in terms of the greatest decision branch EV and disregard any lower values. Use double-hatch marks to indicate a branch from a decision node that is disregarded. You can now calculate the chance event node for the smoke and fire detector development outcome. The input from the â€Å"success† branch is $675,000 x 0. 5. And the input from the â€Å"failure† branch remains at: (-$100,000) x 0. 5. Therefore, the EV = ($675,000 x 0. 5) + (-$100,000 x 0. 5) = $287,500. See figure 2. 4. 2. Figure 2. 4. 2 The calculation in figure 2. 4. 2 is an example of successively calculating the expected values from endpoints back through branches and nodes. Such a rollback calculation takes the EV from a given node and uses that value as a payoff input for the prior node. 12 Decision Trees A Primer for Decision-making Professionals 2. 4. 3 Analyze the changes The motion detector has now become the better choice. The new information dramatically reduces the EV for the smoke and fire detector. What is the main reason for the lower EV? One million dollars revenue is still possible with a commercial grade safety certification, but the likelihood of that outcome is only 30%. Substantial revenue of $800,000 with a 60% outcome is still possible with a residential grade certification. However, that is not enough to offset the resulting lower EV at this node. Since you must use this EV as the input for the development outcome chance node (with only a 50% chance of success) the overall EV for the smoke and fire detector falls below that of the motion detector. The certification process itself is not the culprit in reducing the EV for the smoke and fire detector. The $5000 investment cost barely affects the EV calculations. The small chance of no certification is also only a small factor. Instead, the main reason is the relatively modest probability of obtaining the optimal commercial certification. This lowered probability multiplied by the anticipated revenue significantly lowers the overall EV for that branch. Even if the probability of obtaining a commercial-grade certification is increased to 50% the resulting EV is still less than that for the motion detector. This analysis suggests two main factors that readily affect the EV for the smoke and fire detector. One factor is anticipated revenue. The other is the chance of obtaining the optimal commercial-grade certification. How much would either factor need to improve in order to make the smoke and fire detector the better decision? You can confidently summarize your report to Really Big Ideas with these presentation points: †¢ The smoke and fire detector is now significantly more risky since greater uncertainty exists in knowing which certification grade may be obtained. †¢ †¢ The smoke and fire detector profits are also potentially lessened, especially if a commercial grade certification is not obtained. Together, this combination of greater risk and potentially fewer profits from a less desirable market significantly reduces the attractiveness of the smoke and fire detector project. Exercise Try different possible payoff and/or probability combinations to raise the EV for the smoke and fire detector. What combinations make this EV superior to the motion detector? 13 Decision Trees A Primer for Decision-making Professionals 3. 0 Basic Concepts You can use the decision tree method by mastering a few basic concepts. Use this section to become familiar with these ideas and notation. If you are using this primer for the first time you will probably find the easiest path is to review the material in the following order. 3. 1 3. 2 3. 3 3. 4 3. Decision tree notation (nodes and branches) Payoff values Outcome probability Expected value Decision tree analysis 3. 1 Decision tree notation (nodes and branches) Any decision includes two or more decision alternatives. Any decision alternative might lead to multiple possible outcomes. One outcome may depend on another, a situation called dependent uncertainty. Decisions may also be linked in a sequence, a condition called sequ ential decisions. Use decision tree notation to keep these myriad paths and possibilities easy to understand and compare. Figure 3. 1 14 Decision Trees A Primer for Decision-making Professionals Example In figure 3. 1 a company is evaluating whether to invest $1M in a project immediately or wait for a marketing report that may affect project development. Two other alternatives are also possible: invest $1M in a fixed yield bond or do nothing. A fixed-yield investment and doing nothing are examples of baseline alternatives: choices that can be used to compare the overall merits of the decision alternatives. 3. 1. 1 Decision nodes and the root node Small squares identify decision nodes. A decision tree typically begins with a given â€Å"first decision. † This first decision is called the root node. For example, the root node in a medical situation might represent a choice to perform an operation immediately, try a chemical treatment, or wait for another opinion. Draw the root node at the left side of the decision tree. 3. 1. 2 Chance nodes Small circles identify chance nodes; they represent an event that can result in two or more outcomes. In this illustration two of the decision alternatives connect to chance nodes. Chance nodes may lead to two or more decision or chance nodes. 3. 1. 3 Endpoints An endpoint, or termination node, indicates a final outcome for that branch. Small triangles identify endpoints. Show an endpoint by touching one point of the triangle to the branch it terminates. 3. 1. 4 Branches Lines that connect nodes are called branches. Branches that emanate from a decision node (and towards the right) are called decision branches. Similarly, branches that emanate from a chance node (and towards the right) are called chance branches. In other words, the node that precedes a branch identifies the branch type. A branch can lead to any of the three node types: decision node, chance node, or endpoint. Tip Draw branches from the root node with a generous amount of space between the branches. As branches extend outwards they may spawn any number of additional nodes and branches. 15 Decision Trees A Primer for Decision-making Professionals Start with enough room between branches to easily accommodate the alternatives and outcomes that may result. 3. 2 Payoff values The payoff value is equivalent to the net profit (or net loss) expected at the end of any outcome. Write payoff values at their respective branch endpoints. Although you can express payoff in various ways, it is common to use monetary units in most business applications. Payoff is the difference etween investment cost and gross revenue. This primer adopts the convention of indicating investment costs as negative values to simplify calculating payoff values. Payoff values can be positive or negative. Negative payoff values indicate a net loss. Tip Write the investment cost associated with a decision alternative on the branch. This helps keep the cost in mind when calculating the payoff values. Also write the inve stment cost as a negative value to show that it must reduce any projected gross revenue. Figure 3. 2 Example Figure 3. 2 shows the expected payoffs at two endpoints. The fixed-yield investment results in $1,050,000 revenue, and therefore a $50,000 payoff. The payoff for doing nothing is $0. The other branches lead to chance nodes at this stage of the decision tree. You can assign payoff values only after these chance nodes lead to endpoints. 16 Decision Trees A Primer for Decision-making Professionals 3. 3 Outcome probability A chance node leads to two or more outcomes, each outcome represented by a new branch. As with a game of chance, an outcome has a particular probability of happening. The total of all outcomes for a given chance node must equal 100% (or 1. ). A standard decision tree convention expresses probabilities as decimal fractions in parentheses at the chance branches. Figure 3. 3 Example In Figure 3. 3, the decision alternative to develop a project immediately can lead to one of three outcomes. The company has determined that there is a 20% chance that the project can meet all the criteria for success in international and domestic m arkets, but a 50% chance that the project will only meet the criteria for the domestic market. In addition, is a 30% chance 17 Decision Trees A Primer for Decision-making Professionals hat the project will not meet enough criteria for either market as a result of insufficient information. The company can also wait for a marketing study before developing the project. The marketing information may help the company create a successful project. But the information may also suggest unfavorable conditions that the company probably cannot overcome. The company uses its best judgment and guess, with a 50% favorable and a 50% unfavorable outcome. The decision tree shows these probabilities as decimal fractions in parentheses on their respective chance branches. 3. 4 Expected value Expected value (EV) is a way to measure the relative merits of decision alternatives. The expected value term is a mathematical combination of payoffs and probabilities. You calculate the expected values after all probabilities and payoff values are identified. The goal of the calculations is to find the EV for each decision alternative emerging from the root node. For the purposes of this primer, the decision alternative with the highest EV is the best choice. See figure 3. 4. Although you can apply the formal definition of expected value, in practice you can calculate EV calculations by applying the following rules. To calculate EV, start from the endpoints and work back towards the root. An easy way to find expected values is to calculate an EV for each terminated branch, then each chance node and each decision node. †¢ For a terminated decision branch, EV is equal to the payoff. †¢ †¢ †¢ For a terminated chance branch, EV is the product of its payoff and probability. For a chance node, EV is the sum of each chance branch payoff multiplied by the probability for that payoff. For a decision node, EV is the greater EV value of any decision branch. Mark the lower value EV branches with double-hatch marks to disregard these branch paths. Since the root node is also the first decision node, the decision alternative with the greater EV is the overall best decision. As the calculations are carried from right to left, use a â€Å"resolved† EV at any node type as the payoff â€Å"input† at the node closer to the root. †¢ 18 Decision Trees A Primer for Decision-making Professionals Figure 3. 4 Tip Start an EV calculation from the endpoint and then proceed from right to left. The EV for a node becomes the payoff â€Å"input† for the subsequent EV calculation to the left. For example, in figure 3. , use the EV for the topmost decision node (types of markets to enter) as an input to calculate the chance node (criteria outcomes). Example In figure 3. 4, calculate the EV for the decision alternative to develop the project by following the given EV rules: †¢ Decision node (â€Å"international and domestic marketing† vs. â€Å"domestic marketing only†). The EV is the greatest value giv en by all the decision branches, $3,000,000. This value then becomes the payoff â€Å"input† for the next node to the left. †¢ Chance node (â€Å"all criteria† vs. â€Å"domestic criteria only† vs. â€Å"not enough criteria†). [$3,000,000 x 0. ] + [$500,000 x 0. 5] + [(-$1,000,000) x 0. 3] = EV = $550,000. 19 Decision Trees A Primer for Decision-making Professionals This value becomes the payoff â€Å"input† for this alternative when considering the root node. †¢ By a similar calculation, the EV for the alternative to wait for the report before deciding whether or not to develop the project is EV = $750,000. This value becomes the payoff â€Å"input† for this alternative when considering the root node. The EV for the alternative to invest the capital in a fixed-yield investment is just the payoff value, EV = $50,000. The EV for doing nothing is EV = $0. †¢ †¢ 3. Decision tree analysis The EV at the root node shows that th e decision to wait for the marketing report is the best decision. This result may come as a surprise. You can better understand the result after calculating expected values. Example Before the decision tree in Figure 3. 4 is analyzed you may be tempted to assume that the decision to develop the project immediately is the better choice. After all, the project will only cost $1,000,000 instead of a rushed cost of $1,500,000. Furthermore, there are fewer complications to consider, like waiting to determine the potential for international distribution. The EV for the decision alternative to wait for the report is complicated by two major chance factors. One factor is that the company knows that waiting makes finding an international distributor more difficult than if the project begins immediately. The company has determined that the likelihood of finding an international distributor is less certain (by 50%) if they wait for the report. The other chance factor is the information in the marketing report. The company estimates that the marketing report has a 50% chance of delivering favorable data which will help project development. Two or more chance nodes directly connected in this way indicate a dependent uncertainty, a condition that can readily be evaluated through decision tree analysis. Another complication is that rushing development raises development costs by a third, to ($1,500,000), and this alone reduces the payoff for the international and domestic marketing by $500,000. The decision tree method requires probabilities for all chance outcomes. In this example, the successive chance outcomes of waiting for report results and then securing an international distributor reduce the EV along the branch path. But a similar analysis of the competing decision alternative reveals important information. Without the benefit of the marketing report the chances of â€Å"getting it right† for the 20 Decision Trees A Primer for Decision-making Professionals international market are fairly low, at 20%. This factor significantly weakens the value of that branch. This alternative is also risky; there is a 30% chance that the company will lose all investment costs. The absence of reliable market information means that the project may not meet criteria for success in any market. Figure 3. 5 The analyst can sum up the decision tree analysis with the following major presentation points and with the decision tree in figure 3. 5. †¢ The international market potential is $3,000,000 in revenue, while the domestic market is only $500,000. †¢ †¢ †¢ Immediate project development costs only $1,000,000. Waiting to develop the project results in rush costs, pushing the total to $1,500,000. Marketing information plays the most important role in the potential success of this project. In the absence of valid marketing data, the chance for success in the international market is poor (20%) and the chance for complete failure is sifnificant (30%). These risk factors significantly reduce the potential for product success. 21 Decision Trees A Primer for Decision-making Professionals †¢ Waiting for the marketing report can complicate project development. There is a 50% chance that the report will be favorable enough to proceed. Waiting also reduces the chance (by 50%) for recruiting a distributor in time to capture the international market. However, these risk factors of waiting do not affect the chance of success as much as the absence of marketing data. Therefore the best decision, given the known assumptions, uncertainties, and information, is to wait for the results of the marketing report before deciding to develop the project. †¢ Exercise If you haven’t done so already, review the Decision Scenario exercise. 22 Decision Trees A Primer for Decision-making Professionals 4. 0 Glossary The terms given in this glossary can be applied for business applications and this primer. Other applications such as medicine, artificial intelligence, or general problem solving may use non-monetary value calculations. Figure 4. 0 Branch: A particular decision alternative or chance outcome is called a branch. A branch representing a decision alternative emanates from a decision node. A chance branch (chance outcome) emanates from a chance node. Branch path: A branch path is a series of connected branches leading from a decision node through any given endpoint. Chance branch (chance outcome): A chance branch is one of the possible outcomes emanating from a chance branch. In a decision tree two or more chance branches are lines drawn to the right from a chance node. Chance node, or chance event node: A chance node identifies an event in a decision tree where a degree of uncertainty exists. A chance node represents at least two possible outcomes. Chance nodes are shown by small circles in a decision tree. Cost: A cost is any monetary expense required for a particular decision alternative or that must be paid at a particular chance outcome. Typical cost examples are investments (on decision branches) and penalties (on chance branches). In this primer, investment costs are shown as negative values. 23 Decision Trees A Primer for Decision-making Professionals Data mining: Data mining is a process that uses software to explore information stored in databases for trends and patterns. Decision alternative: Any decision involves a choice between two or more decision alternatives. In a decision tree, a branch emanating from a decision node represents each decision alternative. Decision branch: A decision branch represents a particular decision alternative. In a decision tree, two or more decision branches are lines drawn to the right from a decision node. Decision node: A decision node represents a location on a decision tree where a decision between at least two possible alternatives can be made. Decision nodes are indicated by small squares in a decision tree. Decision strategy: A decision strategy is a particular branch path in a decision tree and includes all the decisions and chance events along that branch path. A decision tree generally includes two or more possible decision strategies. One decision strategy is generally found to be the â€Å"preferred decision strategy† since decision strategies can be compared by computing their respective expected values (EV). Decision tree: A decision tree is a diagram used to describe decision alternatives and chance events. Decision tree analysis: Decision tree analysis is the process of evaluating alternative decision alternatives emanating from the root node. The analysis requires calculating and then comparing expected values. The analysis can also involve making adjustments to probabilities and payoff values to determine how changes to those values may affect expected values. Decision tree notation: A set of graphic symbols and conventions used to describe elements in a decision tree. Commonly used decision tree notation includes decision nodes, chance nodes, endpoints, branches, and double-hatch marks. Dependent uncertainty: A dependent uncertainty is a condition whereby a chance event depends on a prior chance event. For example, if the chance of event â€Å"B† will occur depends on the chance that event â€Å"A† will occur, then some of the uncertainty associated with â€Å"B† depends on â€Å"A. † In a decision tree, a chance node that is directly connected to another chance node indicates a dependent uncertainty. Double-hatch marks: Double-hatch marks are a pair of small lines that are placed over a branch to indicate that particular branch is not to be considered in an expected value calculation. Endpoint: An endpoint is a node that terminates a branch (and also a branch path). In a decision tree, an endpoint is drawn as a small triangle, with one apex connected to the branch. The endpoint is the location where a payoff value is identified. A decision tree is â€Å"terminated† when all the branch paths result in an endpoint with a payoff value. Expected value: Expected value is a criterion for making a decision. Expected value is a mathematical term that combines the payoffs and probabilities of possible chance outcomes for a decision alternative. Technical note: The expected value represents the â€Å"average payoff value† expected if a 24 Decision Trees A Primer for Decision-making Professionals decision were to be repeated many times. The term depends on the relative likelihood of events occurring if the decision were repeated many times while the circumstances remain constant. Many real-world decisions do not have the advantage of being repeatable. Nevertheless, probabilities can still be assigned to outcomes based on information from expert judgment and other means of risk analysis. Such methods are beyond the scope of this primer. For the purposes of this primer assume that the examples use realistic probabilities from reliable sources. EV: EV is an abbreviation for expected value. Investment cost: An investment cost is the monetary amount to be allocated at a decision branch. In this primer, investment costs are shown as negative values. Node: A node is a symbol in a decision tree indicating decision alternatives, chance outcomes, or a branch termination. Payoff or payoff value: A payoff is a monetary amount that will be earned at the conclusion of a branch path. Payoff, also called net profit in business applications, is the difference between the costs and the gross revenue earned. A positive payoff is equivalent to a positive net profit. A negative payoff is equivalent to a net loss. Rollback or rollback calculation: Rollback is the process of successively calculating expected value by beginning at an endpoint and calculating subsequent expected values back towards the root node. Return on investment: Return on investment (ROI) is another term for payoff (or net profit or loss). Root node: The root node is the initial decision node from which a decision tree is established. Sequential decision: A sequential decision is a situation in which more than one decision may be required before a decision tree can be terminated. All but the simplest decision trees contain sequential decisions. Spreadsheet: A spreadsheet is a software application used for managing multiple calculations. Microsoft Excel ® is the leading spreadsheet application on Windows and Mac OS operating systems. Termination node: A termination node is an endpoint. 25 Decision Trees A Primer for Decision-making Professionals 5. 0 More to Explore Decision tree software spans low-cost spreadsheet plug-ins to server-mediated applications suites. Students and casual users may find the free trial offerings from Decision Support Services, Visionary Tools, or Lumenaut particularly useful. †¢ Lumenaut Lumenaut is a Microsoft Excel plug-in. The company offers a free trial and a free student version. http://www. lumenaut. com/ †¢ Salford Systems TreeNet for Windows is among other decision analysis products used for data mining in complex database systems. http://www. salford-systems. com/ Treeplan. com (Decision Support Services) TreePlan is a low cost Microsoft Excel plug-in that works on Windows or Macintosh. A free trial version is available for 15 days. The plug-in is $29, or can be purchased as part of a low cost suite of products. http://www. treeplan. com/ Vanguard Software Corporation Vanguard Studio is a customizable software tool aimed at business development. Single user licenses begin at $1,000. The company web site also offers a short introduction to decision trees. http://www. vanguardsw. com/ Visionary Tools Occam’s Tree is a stand-alone application (Windows-only). This small German company offers a free trial version and a single license for $88. http://www. visionarytools. com/ †¢ †¢ †¢ You can find other information on decision trees and related decision How to cite Decision Tree, Essay examples Decision Tree Free Essays Trees are useful tools for helping you to choose between several courses of action. They provide a highly effective structure within which you can explore options, and investigate the possible outcomes of choosing those options. They also help you to form a balanced picture of the risks and rewards associated with each possible course of action. We will write a custom essay sample on Decision Tree or any similar topic only for you Order Now This makes them particularly useful for choosing between different strategies, projects or investment opportunities, particularly when your resources are limited.How to Use the Tool You start a Decision Tree with a decision that you need to make. Draw a small square to represent this on the left hand side of a large piece of paper, half way down the page. From this box draw out lines towards the right for each possible solution, and write a short description of the solution along the line. Keep the lines apart as far as possible so that you can expand your thoughts. At the end of each line, consider the results. If the result of taking that decision is uncertain, draw a small circle. If the result is another decision that you need to make, draw another square.Squares represent decisions, and circles represent uncertain outcomes. Write the decision or factor above the square or circle. If you have completed the solution at the end of the line, just leave it blank. Starting from the new decision squares on your diagram, draw out lines representing the options that you could select. From the circles draw lines representing possible outcomes. Again make a brief note on the line saying what it means. Keep on doing this until you have drawn out as many of the possible outcomes and decisions as you can see leading on from the original decisions.An example of the sort of thing you will end up with is shown in Figure 1: Once you have done this, review your tree diagram. Challenge each square and circle to see if there are any solutions or outcomes you have not considered. If there are, draw them in. If necessary, redraft your tree if parts of it are too congested or untidy. You should now have a good understanding of the range of possible outcomes of your decisions. Evaluating Your Decision Tree Now you are ready to evaluate the decision tree.This is where you can work out which option has the greatest worth to you. Start by assigning a cash value or score to each possible outcome. Make your best assessment of how much you think it would be worth to you if that outcome came about. Next look at each circle (representing an uncertainty point) and estimate the probability of each outcome. If you use percentages, the total must come to 100% at each circle. If you use fractions, these must add up to 1. If you have data on past events you may be able to make rigorous estimates of the probabilities.Otherwise write down your best guess. This will give you a tree like the one shown in Figure 2: Calculating Tree Values Once you have worked out the value of the outcomes, and have assessed the probability of the outcomes of uncertainty, it is time to start calculating the values that will help you make your decision. Start on the right hand side of the decision tree, and work back towards the left. As you complete a set of calculations on a node (decision square or uncertainty circle), all you need to do is to record the result.You can ignore all the calculations that lead to that result from then on. Calculating The Value of Uncertain Outcome Nodes Where you are calculating the value of uncertain outcomes (circles on the diagram), do this by multiplying the value of the outcomes by their probability. The total for that node of the tree is the total of these values. In the example in Figure 2, the value for ‘new product, thorough development’ is: 0. 4 (probability good outcome) x $1,000,000 (value) =| $400,000| 0. 4 (probability moderate outcome) x ? 0,000 (value) =| $20,000| 0. 2 (probability poor outcome) x ? 2,000 (value) =| $400| +| $420,400| Figure 3 shows the calculation of uncertain outcome nodes: Note that the values calculated for each node are shown in the boxes. Calculating the Value of Decision Nodes When you are evaluating a decision node, write down the cost of each option along each decision line. Then subtract the cost from the outcome value that you have already calculated. This will give you a value that represents the benefit of that decision.Note that amounts already spent do not count for this analysis – these are ‘sunk costs’ and (despite the emotional cost) should not be factored into the decision. When you have calculated these decision benefits, choose the option that has the largest benefit, and take that as the decision made. This is the value of that decision node. Figure 4 shows this calculation of decision nodes in our example: In this example, the benefit we previously calculated for ‘new product, thorough development’ was $420,400. We estimate the future cost of this approach as $150,000.This gives a net benefit of $270,400. The net benefit of ‘new product, rapid development’ was $31,400. On this branch we therefore choose the most valuable option, ‘new product, thorough development’, and allocate this value to the decision node. Result By applying this technique we can see that the best option is to develop a new product. It is worth much more to us to take our time and get the product right, than to rush the product to market. And it’s better just to improve our existing products than to botch a new product, even though it costs us less.Key Points Decision trees provide an effective method of decision making because they: * Clearly lay out the problem so that all options can be challenged. * Allow us to analyze the possible consequences of a decision fully. * Provide a framework to quantify the values of outcomes and the probabilities of achieving them. * Help us to make the best decisions on the basis of existing information and best guesses. As with all decision making methods, decision tree analysis should be used in conjunction with common sense – decision trees are just one important part of your decision making tool kit. How to cite Decision Tree, Papers

Information About the Nizamuddin Dargah free essay sample

Sufi: (Etymology: Worship, Wool) Follower of Islam in a liberal way [spiritual side] * Sufism was born out of necessity * Ulemah were the rigid people who followed Islam. They created rules. * NIZAMUDDIN gave people a lot of freedom * Teacher in Islam is known as PIR. * Student in Islam is known as MUREED. * During Nizamuddin’s time crime was at it’s lowest. * FIRST SUFI SAINT- Moinuddin Chisti * CHISTI SILSILA- Named after people who propagated this. The people had come from a place called Chist * Nizamuddin Auliyah was the 4th Sufi saint. HAZRAT NIZAMUDDIN AULIYAH * He was born in 1238 * Lived in Badaun for 20 years * Hyaspur was its original name. * Nizamuddin had established Khangah. * He was the first saint to go against rigidity. * Treated everyone equally. * Alauddin Khilji tried to become his Mureed (student) * Hyasuddin Tughlaq was jealous of him * Hazrat Amir Khusrao was Nizamuddin’s favorite Mureed. * Khusrao was the only one who had the permission to enter Nizamuddin’s Khangah anytime. We will write a custom essay sample on Information About the Nizamuddin Dargah or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page It was during his time that there was the biggest langar used to take place. * He kept a roza for his whole life AMIR KHUSRAO * He was a businessman, poet, scientist, and musician. Excelled in all the fields. * Invented Tabla and Sitar. * Known as the father of Urdu language. * Died after 6 months of the death of his pir. * When a saint dies, the day is celebrated. Belief- â€Å"When a saint dies, he is said to be united with his beloved(God)† * Qawali was originally known as Sama TOMB OF AMIR KHUSRAO * Made of red sandstone and marble * Quran is engraved on the walls. Red sandstone is like a dressing on the wall. The wall is not actually made up of red sandstone. WHY IS REDSTONE USED? Red sandstone is a dressing to make it attractive. Also red sandstone is very easy to be engraved. Stone – carved and made a Jaali. FAMILY TOMB OF ADGAH KHAN * Tiles are not available anymore. Not able to restore. * The artisans who made the tomb are not available anymore. * The work is very lucrative * On the dome there is a squinch. * A squinch is a structure where a circle is fitted on a square. * Cenotaphs are made of marble. Walls are made of mortar lime – fixing material [Made of rice, dal, jaggery etc. ] MAIN MOSQUE * Thursday is day of congregation prayer. * Built by son of Alauddin Khilji * People pray facing a wall, facing Mecca * Central arch called a mehrab * Verse from a Quran – Inayat * Domes, arches and other features of Islamic architecture can be seen. * The priest is known as Imam. * The architect ure: The base is a square, then arches and a figure of 16 sides and then a dome is built. BAULI * A Bauli is a well with steps leading to it. * The only one in Delhi which always has water.

Accounting Theory Management

Questions: Jimmy is the chief accountant at clothing retailer King Ltd and has been in this role for around 10 years. King has a June 30 year end and Jimmy is finalising the year end accounts. In finalising the inventory valuation Jimmy has a discussion with the warehouse manager. Jimmy is informed of the existence of a large amount of slow-moving stock. A closer inspection of the stock reveals that it is ten months old and would normally have been written down several months earlier if normal procedure had been followed. Jimmy decides to follow up the issue of the stock valuation with the managing director Peter Gladstone. It is well known within the company that Peter is also a key shareholder of King. Jimmy is suspicious that Peter may have given a directive to maintain inventory values. Peter informs Jimmy that there is no need to write down the stock in the year end accounts. Jimmy suspects, however, that Peter wants the balance sheet to carry inflated stock values because he wants to sell King on terms advantageous to the shareholders. Peter goes on to tell Jimmy that he is aware of a potential buyer who is looking to inject capital into the business and that if the sale proceeds then all employees will hold onto their jobs and that Jimmy will receive a substantial pay increase. Required: a) Define the normative ethical perspectives of teleology and deontology. b) From an ethical egoist perspective, what would be an appropriate course of action for Jimmy? Justify your choice. c) Would your answer to b) be different if Jimmy pursued utilitarianism? Justify your position. d) Advise Jimmy of an appropriate course of action from a deontological ethical perspective. Outline why it is based on deontological ethics. Answers: Overview The selected news article, i.e. https://www.abc.net.au/news/2016-02-03/nsw-accountant-facing-fraud-charges/7137160 (Refer to Appendix) focuses largely on the fraud charges that were posed against an accountant named Nicholas James Ellis of Lake Macquarie in New South Wales. The Australian Securities and Investments Commission (ASIC) charged 44 years old Nicholas James Ellis, with an allegation of misappropriating thousands of dollars. It was also evident through investigation that he had committed such offences of fraudulence even in the past and that too around 23 times, for which he had to appear before the Downing Centre Local Court. Majority of those cases related to the misleading statements, which he had made regarding his previous investments (Wakatama, 2016). ASIC made the allegations against Ellis as mentioned in this news article was that he was involved in a fraud of misappropriating approximately $857,000from the funds of the inventor during the tenure of his directorship from March 2009 to June 2010. It was also been investigated that he had utilized the money for his personal benefits such as purchasing a home of $3 million. He had also laundered $250,000in paying off to the investors of his previous failed investment, which he used to run personally. All these charges individually can penalize him for a minimum of 5 years up to a maximum level of 10 years of imprisonment. Moreover, in the year 2013, he was also been prohibited from offering financial services for 6 years (Wakatama, 2016). Major Accounting Issues The ethical issue of financial accounting is the foremost decisive aspect notable in this particular case relating to Ellis. The section of ethical concern that is evident in the case of Ellis is the Misappropriation of Assets, which means the accountant (i.e. Ellis) has been using the assets of the company for his own benefits. In ethical concepts, it can also be stated as an embezzlement of the companys funds/assets for personal benefits that largely affects the stakeholders (Freedman, 2016). Another very significant issue that can be found in the case as presented in the news article is the making of misleading and false statements, which is considered a part of the integrity related issue of accounting laws. According to this issue, the professional accountants associated with the corporate sectors need to be well aware of the integrity of their position and the manner they need to present their dealings in the real world. The foremost aspect that the accountant needs to understa nd is the terms of integrity, which involve the need to be truthful, honest and straightforward in managing their professional relationships. They also need to maintain honesty in making statements regarding the financial issues, so that the reports as well as the other financial documents are presented to the stakeholders of the respective company with utmost accuracy. Lack in professionalism is also a very important issue that can be inferred from the case of Ellis as provided in the news article (IFAC, 2006). Accounting Theories Accounting theories refer to the logical interpretations as well as justifications with the support of various principles, which are not only for the evaluation and for supervision of the accounting practices, but also for its development and innovation in the long run. The principles, customs and procedures on which the accounting theories are implemented are actually the Generally Accepted Accounting Principles (GAAP), which has its respective justifiable reasoning. The accounting theories can be categorised under various heads namely, Descriptive Theory, Deductive Accounting Theory, Evaluative Accounting Theory and Generally Accepted Theories among the most important ones (Riahi-Belkaoui, 2004). The theory that relates with the offences of Ellis as presented in the news article can be evaluated with the help of the Inductive Accounting Theory, as it mostly highlights the previously occurred events within an organisation with respect to the accounting perspectives. In the case prov ided, it can be found that Ellis is charged for the ethical offences, which he committed in the past for which he is liable to be penalised (Wakatama, 2016). Application of the Accounting Issue and Theories with the Case The Misappropriation of Assets is a very significant ethical issue of accounting law, which is apparent from the case of Ellis as presented in the news article. As per the article, Ellis withdrawn money from the investors funds and used for his personal needs of buying a house and paying off his personal debts. In both the cases, Nicholas James Ellis had committed offence of Misappropriation of Assets for which he is liable for appropriate punishments as well as penalties for compensation. The violation of ethical laws of accounting has harsh penalties, as it tends to affect a large group of people financially (Freedman, 2016; Wakatama, 2016). Another offence that he committed was making misleading and false statements in the past regarding his previous investments. This offense is likely to have caused problems of inaccuracy in the organisational reports, which also asserts him to be liable for penalties as compensation. This is an issue related to his personal integrity as a profes sional accountant as well as that of the organisation as a whole. This also hampers professionalism as per the accounting laws, which is also a very serious issue as depicted in the news article of Ellis (Wakatama, 2016; IFAC, 2006). Summary From the overall discussion, therefore, it is apparent from the news article on Ellis that he, being a professional accountant had nor adhered to the ethical considerations of the accounting laws and was hence liable for financial penalties as well as punishments for around 23 cases in the past. Most importantly, he was charged by ASIC on the recent case of Misappropriation of Assets, which has been clearly explained in the above discussion with the help of relevant accounting theories as well as the major accounting issues. The logical interpretations and justifications of the issues with relation to the offences of Ellis also clearly depicts the proper understanding of the viability of the punishment as well penalty that he is charged with for his unethical offences in the field of accounting. References FASB. (2005). Proposed statement of financial accounting standards on business combinations file reference 1204-001. EMC, 1-2. FASB. (2005). FASB exposure draft, proposed statement of financial accounting standards, "business combinations, a replacement of FASB statement no. 141". File Reference: 1204-001, 1-5. FASB. (2005). R.K. Company. File Reference: 1204-001, 1. FASB. (2005). Pooling vs Aquisition accounting for merged cooperatives. File Reference 1204-00 J, 1. Freedman, J. (2016). What is an "ethical issue" in financial accounting? Retrieved June 01, 2016, Guerin, K. (2003). Encouraging quality regulation: theories and tools. New Zealand Treasury Working Paper, 1-20. IFAC. (2006). Code of ethics for professional accountants. Ethics, 1104-1213. Posner, R. A. (1974). Theories of economic regulation. Working Paper, 1-44. Riahi-Belkaoui, A. (2004). Accounting theory. Boston: Cengage Learning EMEA. Wakatama, G. (2016). NSW accountant facing fraud charges. Retrieved June 01, 2016, Williams, K. (2005). FASB, IASB publish joint proposals on business combinations. Streetwise, 19.